Question

terms| degree and coefficient
instructions: for each polynomial below, circle the term of the specified degree and write the coefficient of that term in the space provided.
1 3rd degree (5x^{4}-8x^{3}+x^{2}+10x - 15) coefficient
2 2nd degree (a^{3}+a^{2}+3) coefficient
3 4th degree (21x^{8}+16x^{6}+11x^{4}+6x^{2}+1) coefficient
4 1st degree (-6x^{4}+4x^{3}+2x^{2}-x + 1) coefficient
5 6th degree (-x^{4}+7x^{6}+14x^{3}-9x + 10) coefficient
6 5th degree (-a + 7a^{2}+14-5a^{5}+10a^{2}) coefficient
7 2nd degree (b^{4}+2b^{3}+3b^{2}+4b + 5) coefficient
8 1st degree (-3x^{7}+9x^{5}-4x^{3}-6x + 1) coefficient
9 4th degree (-x^{2}y^{2}+xy^{2}+yx - x + y - 2) coefficient
10 3rd degree (5xy^{4}-5xy^{3}+5xy^{2}-5xy) coefficient
11 3rd degree (a^{3}b^{3}c^{3}+a^{2}b^{2}c^{2}+abc) coefficient
12 2nd degree (10xy+4x^{2}y+6xy^{2}+3x^{2}y^{2}) coefficient

Explanation:

Step1: Recall polynomial degree and coefficient

The degree of a term in a polynomial is the sum of the exponents of the variables in that term. The coefficient is the numerical factor of the term.

Step2: Analyze each polynomial

For \(5x^{4}-8x^{3}+x^{2}+10x - 15\) (3rd degree):

The 3rd - degree term is \(-8x^{3}\), and its coefficient is \(-8\).

For \(a^{3}+a^{2}+3\) (2nd degree):

The 2nd - degree term is \(a^{2}\), and its coefficient is \(1\).

For \(21x^{8}+16x^{6}+11x^{4}+6x^{2}+1\) (4th degree):

The 4th - degree term is \(11x^{4}\), and its coefficient is \(11\).

For \(-6x^{4}+4x^{3}+2x^{2}-x + 1\) (1st degree):

The 1st - degree term is \(-x\), and its coefficient is \(-1\).

For \(-x^{4}+7x^{6}+14x^{3}-9x + 10\) (6th degree):

The 6th - degree term is \(7x^{6}\), and its coefficient is \(7\).

For \(-a + 7a^{2}+14-5a^{5}+10a^{2}\) (5th degree):

The 5th - degree term is \(-5a^{5}\), and its coefficient is \(-5\).

For \(b^{4}+2b^{3}+3b^{2}+4b + 5\) (2nd degree):

The 2nd - degree term is \(3b^{2}\), and its coefficient is \(3\).

For \(-3x^{7}+9x^{5}-4x^{3}-6x + 1\) (1st degree):

The 1st - degree term is \(-6x\), and its coefficient is \(-6\).

For \(-x^{2}y^{2}+xy^{2}+yx - x + y - 2\) (4th degree):

The 4th - degree term is \(-x^{2}y^{2}\), and its coefficient is \(-1\).

For \(5xy^{4}-5xy^{3}+5xy^{2}-5xy\) (3rd degree):

The 3rd - degree term is \(-5xy^{2}\), and its coefficient is \(-5\).

For \(a^{3}b^{3}c^{3}+a^{2}b^{2}c^{2}+abc\) (3rd degree):

The 3rd - degree term is \(abc\), and its coefficient is \(1\).

For \(10xy + 4x^{2}y+6xy^{2}+3x^{2}y^{2}\) (2nd degree):

The 2nd - degree term is \(10xy\), and its coefficient is \(10\).

Answer:

1. \(-8\)
2. \(1\)
3. \(11\)
4. \(-1\)
5. \(7\)
6. \(-5\)
7. \(3\)
8. \(-6\)
9. \(-1\)
10. \(-5\)
11. \(1\)
12. \(10\)